Question

Select all of the pieces of information that would tell you x and y have a proportional relationship. Let y represent the distance in meters between a rock and a turtle's current position and x represent the time in minutes the turtle has been moving.

Answer 1

Complete Question:

Select all of the pieces of information that would tell you x and y have a proportional relationship.

Let y represent the distance between a rock and a turtle's current position in meters and x represent the number of minutes the turtle has been moving. y=3x

1. After 4 minutes, the turtle has walked 12 feet away from the rock.

2. The turtle walks for a bit, then stops for a minute before walking again.

3. The turtle walks away from the rock at a constant rate.

Answer:

1. After 4 minutes, the turtle has walked 12 feet away from the rock.

3. The turtle walks away from the rock at a constant rate.

Explanation:

Given

`y = 3x`

Required

Determine which of the options answers the question

Recall that:

`y = distance`

`x = time`

Analyzing the options 1 after the other:

Option 1:

In this option, we have that:

`y = 12`

`x = 4`

Substitute these values of x and y in the given equation

`y = 3x`

`12 = 3 * 4`

`12 = 12`

Because both sides of the equation are equal, this option shows a proportional relationship

Option 2:

The given equation cannot be used to ascertain the information given in this option.

Because for a every time (in minutes) traveled by the turtle, there's a corresponding distance moved.

Option 3:

Recall that

`y = 3x`

Assume
`x = 5`

y would be

`y = 3 * 5`

`y = 15`

Assume
`x = 6`

y would be

`y = 3 * 6`

`y = 18`

For every values of x and corresponding y value, there exist a constant relationship because:

`(y)/(x) = 3`

This implies that the rate at which the turtle moved is 3ft/s and this rate is constant.